Does the 'Retina (hidef) images' option also upgrade menu resolution?
Yes that option means that all graphics, text exported as graphics and photos are output at Retina resolution and will be sharp - exactly the same as native resolution on the iPad. The method works for all hi-def screens on all devices, Android, Windows and OSx/iOS.

With this option on, all graphics and images are exports at normal and hi-res verison (using the normal @2x convention for the filenames). There is javascript on the page that intelligently loads the correct image depending on the screen resolution of the device. So this means your websites is maximally optimized for normal screens so there's no unnecessary downloading of over-resolution images for normal displays,(unlike that Joel example) but also that you get hi-res graphics and photos on on Retina and similar hi-res screens.